4. Consider a society that has three individuals - 1,2 and 3 - and three alternatives - x, y and z. The society has a preference aggregation rule F. In year 2007, the profile of individual preferences were as follows: 1 2 3 y zy Z X X It is known that the rule F satisfies Completeness, Transitivity, Anonymity, Unanimity and Independence of Irrelevant Alternatives. Also, in year 2007, F ranked x strictly above y. Now, we are in year 2008. The individual preferences have changed to: 1 2 3 z | y| y X y ANX (a) How does the society rank between y and x in 2008? (b) How does the society rank between x and z in 2008? Why? Why? (c) How does the society rank between y and z in 2008? Why? (d) What were the social preferences over all three alternatives in 2007?
4. Consider a society that has three individuals - 1,2 and 3 - and three alternatives - x, y and z. The society has a preference aggregation rule F. In year 2007, the profile of individual preferences were as follows: 1 2 3 y zy Z X X It is known that the rule F satisfies Completeness, Transitivity, Anonymity, Unanimity and Independence of Irrelevant Alternatives. Also, in year 2007, F ranked x strictly above y. Now, we are in year 2008. The individual preferences have changed to: 1 2 3 z | y| y X y ANX (a) How does the society rank between y and x in 2008? (b) How does the society rank between x and z in 2008? Why? Why? (c) How does the society rank between y and z in 2008? Why? (d) What were the social preferences over all three alternatives in 2007?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:4. Consider a society that has three individuals - 1,2 and 3 - and three alternatives - x, y and
z. The society has a preference aggregation rule F.
In year 2007, the profile of individual preferences were as follows:
1 2 3
X y Z
y Z V
It is known that the rule F satisfies Completeness, Transitivity, Anonymity,
Unanimity and Independence of Irrelevant Alternatives. Also, in year 2007, F
ranked x strictly above y.
Now, we are in year 2008. The individual preferences have changed to:
1 2 3
Z
y y
X
Z Z
y X x
(a) How does the society rank between y and x in 2008? Why?
(b) How does the society rank between x and z in 2008? Why?
(c) How does the society rank between y and z in 2008? Why?
(d) What were the social preferences over all three alternatives in 2007?
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